利用互无偏测量构造的可分判据

Separability Criteria via Mutually Unbiased Measurements

利用互无偏测量可以很好地研究量子态的可分问题.首先,利用对角对称态和密度矩阵部分转置正的关系,结合互无偏测量,研究了两体量子系统中2类对角对称态可分性,给出了可分的充要条件.其次,研究了两体量子系统中子系统维数为2的量子态可分性,利用密度矩阵的Bloch表示,以及互无偏测量和群生成元的关系,给出了态可分的必要条件.最后,研究了两体任意维量子系统中量子态的可分性,利用迹范数与向量范数的关系以及互无偏测量和密度矩阵之间的关系,给出了态可分判据,并用具体例子说明可分判据能判别出更多的纠缠态.

Mutually unbiased measurements can be used to study the separability of quantum states.First,centered on the relationship between the diagonal symmetry states and the partial transpose positive of density matrix,combined with mutually unbiased measurements,the separability of two types of diagonal symmetric states in the bipartite quantum systems was studied,and the necessary and sufficient conditions for separability were obtained.Second,the separability of the quantum states in the bipartite quantum systems with 2-dimensional subsystems was studied.Using the Bloch representation of the density matrix and the relationship between the mutually unbiased measurements and the group generators,the necessary condition for separability was obtained.Finally,the separability of general quantum states in bipartite quantum systems was studied.By using the relationship between the trace norm and the vector norm,and the relationship between the mutually unbiased measurements and the density matrix,separability criteria for quantum states was presented.Moreover,this approach can detect more entangled states through some detailed examples.